scholarly journals Toric extremal Kähler-Ricci solitons are Kähler-Einstein

2017 ◽  
Vol 4 (1) ◽  
pp. 179-182 ◽  
Author(s):  
Simone Calamai ◽  
David Petrecca
Keyword(s):  
General Problem ◽  
Short Note ◽  
Kähler Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Toric Manifolds ◽  
Kahler Manifold

Abstract In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.

scholarly journals η-*-Ricci Solitons and Almost co-Kähler Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3200
Author(s):  
Arpan Sardar ◽  
Mohammad Nazrul Islam Khan ◽  
Uday Chand De
Keyword(s):  
Ricci Tensor ◽  
Kähler Manifold ◽  
Ricci Soliton ◽  
Kähler Manifolds ◽  
Ricci Solitons ◽  
Kahler Manifolds ◽  
Kahler Manifold ◽  
New Type ◽  
The Subject

The subject of the present paper is the investigation of a new type of solitons, called η-*-Ricci solitons in (k,μ)-almost co-Kähler manifold (briefly, ackm), which generalizes the notion of the η-Ricci soliton introduced by Cho and Kimura . First, the expression of the *-Ricci tensor on ackm is obtained. Additionally, we classify the η-*-Ricci solitons in (k,μ)-ackms. Next, we investigate (k,μ)-ackms admitting gradient η-*-Ricci solitons. Finally, we construct two examples to illustrate our results.

scholarly journals On Sasaki–Ricci solitons and their deformations

2016 ◽  
Vol 16 (1) ◽  
Author(s):  
David Petrecca
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Kähler Manifold ◽  
Stability Result ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Holomorphic Vector Fields ◽  
Kahler Manifold ◽  
Sasakian Structures

AbstractWe extend to the Sasakian setting a result of Tian and Zhu about the decomposition of the Lie algebra of holomorphic vector fields on a Kähler manifold in the presence of a Kähler-Ricci soliton. Furthermore we apply known deformations of Sasakian structures to a Sasaki-Ricci soliton to obtain a stability result concerning generalized Sasaki-Ricci solitons, generalizing results of Li in the Kähler setting and of He and Sun by relaxing some of their assumptions.

scholarly journals BOUNDING SECTIONAL CURVATURE ALONG THE KÄHLER–RICCI FLOW

2009 ◽  
Vol 11 (06) ◽  
pp. 1067-1077 ◽  
Author(s):  
WEI-DONG RUAN ◽  
YUGUANG ZHANG ◽  
ZHENLEI ZHANG
Keyword(s):  
Sectional Curvature ◽  
Chern Class ◽  
Ricci Flow ◽  
Kähler Manifold ◽  
Ricci Soliton ◽  
Curvature Operator ◽  
Kahler Manifold ◽  
First Chern Class ◽  
Compact Kähler Manifold ◽  
Uniformly Bounded

If a normalized Kähler–Ricci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M, dim ℂ M = n ≥ 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently, the flow will converge along a subsequence to a Kähler–Ricci soliton.

CONFORMAL RICCI SOLITON ON ALMOST CO-KÄHLER MANIFOLD

2020 ◽  
Vol 9 (10) ◽  
pp. 8399-8411
Author(s):  
D. Ganguly ◽  
A. Bhattacharyya
Keyword(s):  
Kähler Manifold ◽  
Ricci Soliton ◽  
Kahler Manifold

scholarly journals Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

A POSITIVITY PROPERTY FOR FOLIATIONS ON COMPACT KÄHLER MANIFOLDS

2006 ◽  
Vol 17 (01) ◽  
pp. 35-43 ◽  
Author(s):  
MARCO BRUNELLA
Keyword(s):  
Kähler Manifold ◽  
Rational Curves ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Canonical Bundle ◽  
Positivity Property ◽  
Kahler Manifold ◽  
Compact Kähler Manifold

We prove that the canonical bundle of a foliation by curves on a compact Kähler manifold is pseudoeffective, unless the foliation is a (special) foliation by rational curves.

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